Step by step
The question
Question: Adult tickets cost $9 and child tickets cost $6.
A cinema sold 3 times as many child tickets as adult tickets.
It made $540.
How many of each ticket did it sell?
1 Find what we know
What do we know?
Two kinds: adult tickets cost $9 each, child tickets cost $6 each.
There are 3 times as many child tickets as adult tickets.
All the money: $540.
What do we want?
How many adult tickets, and how many child tickets.
2 Name the unknown
We know the child tickets from the adult tickets.
So we start with the adult tickets.
We call how many there are x.
There are 3 times as many child tickets as adult tickets.
3 times x: 3x.
Careful!
There are 3 times as many child tickets as adult tickets.
So the child tickets are 3x, not the adult tickets.
Let's put it in a table: how many, the price, and the money.
Adult tickets: x of them, $9 each.
Child tickets: 3x of them, $6 each.
Money = how many times the price.
9 times x is 9x.
6 times all of 3x is 6(3x).
We keep 3x together in brackets.
The total: $540 in all.
3 Write the equation
In words: the adult money plus the child money makes all the money.
So the equation is 9x + 6(3x) = 540.
Now we solve it.
4 Open the brackets
The 6 in front of the bracket multiplies every part inside.
So we write 6 times each part.
Work out each multiplication.
5 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
9x + 18x = 27x.
Now we have 27x = 540.
6 Remove the 27
27x means 27 times x.
We want just x.
To remove times 27, we divide by 27.
We do it on both sides, so they stay equal.
27 divided by 27 is 1.
So just x is left.
540 divided by 27 is 20.
So x = 20!
7 Answer the question
Child tickets: 3x.
3 × 20 = 60.
So 20 adult tickets and 60 child tickets.
8 Check
Let's check in the story.
3 times 20 is 60: 3 times as many, like the story says.
The money: $180 plus $360 makes $540, like the story says.
Does it make sense?
Both are whole numbers, not below 0.
That fits tickets.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.